Categorical Wombling: Detecting Regions of Significant Change in Spatially Located Categorical Variables

摘要: Wombling is a method for discovering boundaries in collection of continuous variables obsmed at the same geographic localities. We extend this to categorical data. A wombling statistic C,, which identi$es areas rapid change, &$ned every pair i = 1,. . , n adjacent localities, and equal average number category mismatches i. use both simulation theory consider or&r statistics Ci under null hypotheses randomness, spatial autocorrelation each variable, but independence between variables. Graph-theoretical derived from C, investigate whether change resemble bmnduries. Computer used study distributions these two hypotheses. The methods are applied linguistic data three European areas. Other potentid applications exist biology, linguistics, anthropology, other social sciences. variable observed set localities may often be profitably viewed as being measured discrete points on an underlying surface. Wombling, first developed by Womble (1951) gene frequencies morphological measurements, later refined Barbujani, Oden, Sokal (1989), technique detecting zones such surfaces. rests upon notion “systemic function” defined over space. At any locality, systemic function absolute values gradients separate surfaces that locality. Mapping space reveals change. Related ideas have been Monmonier (1973) Adams (1970). Neal L Oden senior scientist Applied Biomathnnotics, lnc., Setauket, New York. Robert R distinguished professor ecology evolution State University York Stony Brook. Marie-Jmt?e Fdn postdoctoral research associate Centre dktudes Nordiqws, Universitk Luval, Quebec. Hans Goebl romance linguistics o Salzburg Austria.